Spatial Data and
Cartography (Part 2)

Lecture 17

Dr. Colin Rundel

`sf` object summary

From last time,

sf class is an extension of data.frame / tibble that includes a geometry column
The geometry column is a list column with the sfc class
- This column also tracks the CRS of the geometry (set via st_crs() or transformed by st_transform())
Elements of the geometry column are objects with the sfg class
- S3 class also contains the simple feature geometry type and coordinate type

Plotting

Example Data - NC SIDS

( nc = read_sf(system.file("shape/nc.shp", package="sf"), quiet = TRUE) |> 
    select(-(AREA:CNTY_ID), -(FIPS:CRESS_ID)))

Simple feature collection with 100 features and 7 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
Geodetic CRS:  NAD27
# A tibble: 100 × 8
   NAME        BIR74 SID74 NWBIR74 BIR79 SID79 NWBIR79
   <chr>       <dbl> <dbl>   <dbl> <dbl> <dbl>   <dbl>
 1 Ashe         1091     1      10  1364     0      19
 2 Alleghany     487     0      10   542     3      12
 3 Surry        3188     5     208  3616     6     260
 4 Currituck     508     1     123   830     2     145
 5 Northampton  1421     9    1066  1606     3    1197
 6 Hertford     1452     7     954  1838     5    1237
 7 Camden        286     0     115   350     2     139
 8 Gates         420     0     254   594     2     371
 9 Warren        968     4     748  1190     2     844
10 Stokes       1612     1     160  2038     5     176
# ℹ 90 more rows
# ℹ 1 more variable: geometry <MULTIPOLYGON [°]>

Base Plots

plot(nc)

Geometry Plot

plot(st_geometry(nc), axes=TRUE)

Graticules

plot(nc[,"SID79"], graticule=TRUE, axes=TRUE)

EPSG 3631

plot(st_transform(nc[,"SID79"], 3631), axes=TRUE)

EPSG 3631 w/ Graticules

plot(st_transform(nc[,"SID79"], 3631), graticule=TRUE, axes=TRUE)

EPSG 3631 w/ Lat / long Graticules

plot(st_transform(nc[,"SID79"], 3631), graticule=st_crs(4326), axes=TRUE)

EPSG 3631 w/ 3631 Graticules

plot(st_transform(nc[,"SID79"], 3631), graticule=st_crs(3631), axes=TRUE)

ggplot2

ggplot(nc) + 
  geom_sf(aes(fill=SID79))

ggplot2 + projections

ggplot(st_transform(nc, 3631)) + 
  geom_sf(aes(fill=SID79 / BIR79))

ggplot2 + viridis

ggplot(st_transform(nc, 3631)) + 
  geom_sf(aes(fill=SID79 / BIR79)) +
  scale_fill_viridis_c()

Example Data - Meuse

data(meuse, meuse.riv, package="sp")
(meuse = st_as_sf(meuse, coords=c("x", "y"), crs=28992) |>
  as_tibble() |> st_as_sf())

Simple feature collection with 155 features and 12 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 178605 ymin: 329714 xmax: 181390 ymax: 333611
Projected CRS: Amersfoort / RD New
# A tibble: 155 × 13
   cadmium copper  lead  zinc  elev    dist    om ffreq soil  lime  landuse dist.m
     <dbl>  <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl> <fct> <fct> <fct> <fct>    <dbl>
 1    11.7     85   299  1022  7.91 0.00136  13.6 1     1     1     Ah          50
 2     8.6     81   277  1141  6.98 0.0122   14   1     1     1     Ah          30
 3     6.5     68   199   640  7.8  0.103    13   1     1     1     Ah         150
 4     2.6     81   116   257  7.66 0.190     8   1     2     0     Ga         270
 5     2.8     48   117   269  7.48 0.277     8.7 1     2     0     Ah         380
 6     3       61   137   281  7.79 0.364     7.8 1     2     0     Ga         470
 7     3.2     31   132   346  8.22 0.190     9.2 1     2     0     Ah         240
 8     2.8     29   150   406  8.49 0.0922    9.5 1     1     0     Ab         120
 9     2.4     37   133   347  8.67 0.185    10.6 1     1     0     Ab         240
10     1.6     24    80   183  9.05 0.310     6.3 1     2     0     W          420
# ℹ 145 more rows
# ℹ 1 more variable: geometry <POINT [m]>

( meuse_riv = st_polygon(list(meuse.riv)) |>
    st_sfc() |>
    st_set_crs(28992) |>
    st_as_sf()
)

Simple feature collection with 1 feature and 0 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 178304 ymin: 325698.5 xmax: 182331.5 ymax: 337684.8
Projected CRS: Amersfoort / RD New
                               x
1 POLYGON ((182003.7 337678.6...

Meuse

plot(meuse, pch=16, max.plot=12)

Layering plots

plot(
  meuse_riv, col=adjustcolor("lightblue", alpha.f=1), border = NA, 
  axes=TRUE, graticule=st_crs(4326),
  ylim = c(329500, 334000)
)
plot(meuse[,"lead"], pch=16, add=TRUE)

ggplot2

ggplot() +
  geom_sf(data=meuse_riv, fill="lightblue", color=NA) +
  geom_sf(data=meuse, aes(color=lead), size=1)

ggplot2 - axis limits

ggplot() +
  geom_sf(data=meuse_riv, fill="lightblue", color=NA) +
  geom_sf(data=meuse, aes(color=lead), size=1) +
  ylim(50.95, 50.99)

ggplot2 - axis limits

ggplot() +
  geom_sf(data=meuse_riv, fill="lightblue", color=NA) +
  geom_sf(data=meuse, aes(color=lead), size=1) +
  ylim(329500, 334000)

ggplot2 - bounding box

ggplot() +
  geom_sf(data=st_sf(meuse_riv), fill="lightblue", color=NA) +
  geom_sf(data=meuse, aes(color=lead), size=1) +
  ylim(st_bbox(meuse)["ymin"], st_bbox(meuse)["ymax"])

Geometry Predicates

DE-9IM

Spatial predicates

st_within(a,b):

\[ \begin{bmatrix} T & * & F \\ * & * & F \\ * & * & * \end{bmatrix} \]

st_touches(a,b):

\[ \begin{bmatrix} F & T & * \\ * & * & * \\ * & * & * \end{bmatrix} \cup \begin{bmatrix} F & * & * \\ T & * & * \\ * & * & * \end{bmatrix} \cup \begin{bmatrix} F & * & * \\ * & T & * \\ * & * & * \end{bmatrix} \]

Sparse vs Full Results

st_intersects(ncc[20:30,], air) %>% str()

List of 11
 $ : int(0) 
 $ : int(0) 
 $ : int(0) 
 $ : int(0) 
 $ : int(0) 
 $ : int 268
 $ : int 717
 $ : int(0) 
 $ : int(0) 
 $ : int(0) 
 $ : int(0) 
 - attr(*, "predicate")= chr "intersects"
 - attr(*, "region.id")= chr [1:11] "1" "2" "3" "4" ...
 - attr(*, "remove_self")= logi FALSE
 - attr(*, "retain_unique")= logi FALSE
 - attr(*, "ncol")= int 940
 - attr(*, "class")= chr [1:2] "sgbp" "list"

st_intersects(ncc, air, sparse=FALSE) %>% str()

 logi [1:100, 1:940] FALSE FALSE FALSE FALSE FALSE FALSE ...

Examples

Which counties have an airport?
Which counties are adjacent to Durham County?
Which counties have more than 4 neighbors?

ncc = read_sf("data/gis/nc_counties/", quiet=TRUE) |> st_transform(3631)
air = read_sf("data/gis/airports/", quiet=TRUE) |> st_transform(3631)
hwy = read_sf("data/gis/us_interstates/", quiet=TRUE) |> st_transform(3631)

Data

Which counties have an airport?

ncc |>
  select(COUNTY, geometry) |>
  mutate(
    airports = st_intersects(ncc, air) |> unclass(),
    n = purrr::map_int(airports, length),
    airport_names = purrr::map_chr(
      airports, 
      ~ paste(air$AIRPT_NAME[.x], collapse=", ") |> str_to_title()
    )
  ) |>
  filter(n > 0) |> 
  arrange(desc(n))

Which counties have an airport?

Simple feature collection with 16 features and 4 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 257742.1 ymin: 20311.68 xmax: 930352.8 ymax: 280007
Projected CRS: NAD83(NSRS2007) / North Carolina
# A tibble: 16 × 5
   COUNTY                                            geometry airports     n airport_names
   <chr>                                   <MULTIPOLYGON [m]> <list>   <int> <chr>        
 1 Craven County      (((815892.7 133083, 815712 132990.1, 8… <int>        2 Cherry Point…
 2 Cumberland County  (((634732.8 168173.4, 634781.1 168150.… <int>        2 Pope Air For…
 3 Forsyth County     (((480355.6 279558.3, 480622.3 279554.… <int>        1 Smith Reynol…
 4 Guilford County    (((516951.1 278659.3, 517346.4 278644.… <int>        1 Piedmont Tri…
 5 Dare County        (((925331.7 195868.4, 925150.9 195670.… <int>        1 Dare County …
 6 Wake County        (((635486.1 258098.2, 635729.3 258098.… <int>        1 Raleigh-Durh…
 7 Pitt County        (((756611.7 231604, 757952.2 231061.2,… <int>        1 Pitt-Greenvi…
 8 Catawba County     (((416107.9 232317.8, 416052.5 231678.… <int>        1 Hickory Regi…
 9 Buncombe County    (((304720 234673.2, 304825.7 234591.9,… <int>        1 Asheville Re…
10 Wayne County       (((700246.7 204130.8, 700364.9 204087.… <int>        1 Seymour John…
11 Mecklenburg County (((446654.6 196384.3, 446836 196381, 4… <int>        1 Charlotte/Do…
12 Moore County       (((577854 196164.2, 577890.8 195888.4,… <int>        1 Moore County…
13 Cabarrus County    (((453375.4 196276.2, 453511.2 196262.… <int>        1 Concord Regi…
14 Lenoir County      (((748430.8 185813.4, 748462.9 185245.… <int>        1 Kinston Regi…
15 Onslow County      (((771041.7 95091.1, 771303.3 95086.16… <int>        1 Albert J Ell…
16 New Hanover County (((708050.4 27602.3, 707840.5 27355.98… <int>        1 Wilmington I…

Which counties neighbor Durham County?

ncc |>
  select(COUNTY, geometry) |>
  mutate(
    touch_durham = st_touches(ncc, ncc |> filter(COUNTY == "Durham County")) |> unclass(),
    n_touches = map_int(touch_durham, length)
  ) |>
  filter(n_touches > 0)

Simple feature collection with 5 features and 3 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 559195.8 ymin: 195938.7 xmax: 676918.6 ymax: 309925.7
Projected CRS: NAD83(NSRS2007) / North Carolina
# A tibble: 5 × 4
  COUNTY                                                   geometry touch_durham n_touches
* <chr>                                          <MULTIPOLYGON [m]> <list>           <int>
1 Person County    (((611470.1 309761.9, 611935.8 309762, 612123.9… <int [1]>            1
2 Granville County (((658298.4 309773.1, 658351.6 309762.4, 658405… <int [1]>            1
3 Orange County    (((586623.3 276687.6, 587090.7 276675.3, 587378… <int [1]>            1
4 Wake County      (((635486.1 258098.2, 635729.3 258098.9, 635815… <int [1]>            1
5 Chatham County   (((589371.3 235671.1, 589560.8 235648.5, 589606… <int [1]>            1

Which counties have more than 4 neighbors?

ncc |>
  mutate(
    neighbors = st_touches(ncc) |> unclass(),
    n_neighbors = map_int(neighbors, length)
  ) |>
  ggplot(aes(fill = n_neighbors > 4)) +
    geom_sf()

Geometry Manipulation

Casting

(nc_pts = st_cast(nc, "MULTIPOINT"))

Simple feature collection with 100 features and 7 fields
Geometry type: MULTIPOINT
Dimension:     XY
Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
Geodetic CRS:  NAD27
# A tibble: 100 × 8
   NAME        BIR74 SID74 NWBIR74 BIR79 SID79 NWBIR79                            geometry
   <chr>       <dbl> <dbl>   <dbl> <dbl> <dbl>   <dbl>                    <MULTIPOINT [°]>
 1 Ashe         1091     1      10  1364     0      19 ((-81.47276 36.23436), (-81.54084 …
 2 Alleghany     487     0      10   542     3      12 ((-81.23989 36.36536), (-81.24069 …
 3 Surry        3188     5     208  3616     6     260 ((-80.45634 36.24256), (-80.47639 …
 4 Currituck     508     1     123   830     2     145 ((-76.00897 36.3196), (-76.01735 3…
 5 Northampton  1421     9    1066  1606     3    1197 ((-77.21767 36.24098), (-77.23461 …
 6 Hertford     1452     7     954  1838     5    1237 ((-76.74506 36.23392), (-76.98069 …
 7 Camden        286     0     115   350     2     139 ((-76.00897 36.3196), (-75.95718 3…
 8 Gates         420     0     254   594     2     371 ((-76.56251 36.34057), (-76.60424 …
 9 Warren        968     4     748  1190     2     844 ((-78.30876 36.26004), (-78.28293 …
10 Stokes       1612     1     160  2038     5     176 ((-80.02567 36.25023), (-80.45301 …
# ℹ 90 more rows

plot(st_geometry(nc), border='grey')
plot(st_geometry(nc_pts), pch=16, cex=0.5, add=TRUE)

Casting - POINT

st_cast(nc, "POINT")

Simple feature collection with 2529 features and 7 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
Geodetic CRS:  NAD27
# A tibble: 2,529 × 8
   NAME  BIR74 SID74 NWBIR74 BIR79 SID79 NWBIR79             geometry
   <chr> <dbl> <dbl>   <dbl> <dbl> <dbl>   <dbl>          <POINT [°]>
 1 Ashe   1091     1      10  1364     0      19 (-81.47276 36.23436)
 2 Ashe   1091     1      10  1364     0      19 (-81.54084 36.27251)
 3 Ashe   1091     1      10  1364     0      19 (-81.56198 36.27359)
 4 Ashe   1091     1      10  1364     0      19 (-81.63306 36.34069)
 5 Ashe   1091     1      10  1364     0      19 (-81.74107 36.39178)
 6 Ashe   1091     1      10  1364     0      19 (-81.69828 36.47178)
 7 Ashe   1091     1      10  1364     0      19  (-81.7028 36.51934)
 8 Ashe   1091     1      10  1364     0      19    (-81.67 36.58965)
 9 Ashe   1091     1      10  1364     0      19  (-81.3453 36.57286)
10 Ashe   1091     1      10  1364     0      19 (-81.34754 36.53791)
# ℹ 2,519 more rows

plot(st_geometry(nc), border='grey')
plot(st_geometry(st_cast(nc, "POINT")), pch=16, cex=0.5, add=TRUE)

Casting - LINESTRING

st_cast(nc, "MULTILINESTRING")

Simple feature collection with 100 features and 7 fields
Geometry type: MULTILINESTRING
Dimension:     XY
Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
Geodetic CRS:  NAD27
# A tibble: 100 × 8
   NAME        BIR74 SID74 NWBIR74 BIR79 SID79 NWBIR79                            geometry
   <chr>       <dbl> <dbl>   <dbl> <dbl> <dbl>   <dbl>               <MULTILINESTRING [°]>
 1 Ashe         1091     1      10  1364     0      19 ((-81.47276 36.23436, -81.54084 36…
 2 Alleghany     487     0      10   542     3      12 ((-81.23989 36.36536, -81.24069 36…
 3 Surry        3188     5     208  3616     6     260 ((-80.45634 36.24256, -80.47639 36…
 4 Currituck     508     1     123   830     2     145 ((-76.00897 36.3196, -76.01735 36.…
 5 Northampton  1421     9    1066  1606     3    1197 ((-77.21767 36.24098, -77.23461 36…
 6 Hertford     1452     7     954  1838     5    1237 ((-76.74506 36.23392, -76.98069 36…
 7 Camden        286     0     115   350     2     139 ((-76.00897 36.3196, -75.95718 36.…
 8 Gates         420     0     254   594     2     371 ((-76.56251 36.34057, -76.60424 36…
 9 Warren        968     4     748  1190     2     844 ((-78.30876 36.26004, -78.28293 36…
10 Stokes       1612     1     160  2038     5     176 ((-80.02567 36.25023, -80.45301 36…
# ℹ 90 more rows

st_cast(nc, "MULTILINESTRING") |> st_geometry() |> plot()

Grouping Features

nc_state = st_union(nc)
plot(nc_state)

More Grouping

( nc_cut = nc |>
   mutate(X = st_centroid(nc) |> st_coordinates() |> (\(x) x[,1])()) |>
   mutate(region = cut(X, breaks = 5)) )

Simple feature collection with 100 features and 9 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
Geodetic CRS:  NAD27
# A tibble: 100 × 10
   NAME     BIR74 SID74 NWBIR74 BIR79 SID79 NWBIR79                  geometry     X region
 * <chr>    <dbl> <dbl>   <dbl> <dbl> <dbl>   <dbl>        <MULTIPOLYGON [°]> <dbl> <fct> 
 1 Ashe      1091     1      10  1364     0      19 (((-81.47276 36.23436, -… -81.5 (-82.…
 2 Allegha…   487     0      10   542     3      12 (((-81.23989 36.36536, -… -81.1 (-82.…
 3 Surry     3188     5     208  3616     6     260 (((-80.45634 36.24256, -… -80.7 (-80.…
 4 Curritu…   508     1     123   830     2     145 (((-76.00897 36.3196, -7… -76.0 (-77.…
 5 Northam…  1421     9    1066  1606     3    1197 (((-77.21767 36.24098, -… -77.4 (-77.…
 6 Hertford  1452     7     954  1838     5    1237 (((-76.74506 36.23392, -… -77.0 (-77.…
 7 Camden     286     0     115   350     2     139 (((-76.00897 36.3196, -7… -76.2 (-77.…
 8 Gates      420     0     254   594     2     371 (((-76.56251 36.34057, -… -76.7 (-77.…
 9 Warren     968     4     748  1190     2     844 (((-78.30876 36.26004, -… -78.1 (-79.…
10 Stokes    1612     1     160  2038     5     176 (((-80.02567 36.25023, -… -80.2 (-80.…
# ℹ 90 more rows

ggplot(nc_cut) +
  geom_sf(aes(fill=region))

Union via summarize

nc_cut |> 
  group_by(region) |> 
  summarize() |> 
  ggplot() + 
    geom_sf(aes(fill=region))

Affine Transfomations

rotate = function(a) matrix(c(cos(a), sin(a), -sin(a), cos(a)), 2, 2)

ctrd = st_centroid(nc_state)
state_rotate = (nc_state) * rotate(-pi/4)
plot(state_rotate, axes=TRUE)

Scaling Size

ctrd = st_centroid(st_geometry(nc))
area = st_area(nc) |> strip_attrs()

nc_rot = nc
st_geometry(nc_rot) = (st_geometry(nc) - ctrd) * 0.75 + ctrd

plot(nc_rot[,"SID79"])

Highway Example

Highways

ggplot() +
  geom_sf(data=ncc) +
  geom_sf(data=hwy, col='red')

NC Interstate Highways

hwy_nc = st_intersection(hwy, ncc)

ggplot() + 
  geom_sf(data=nc) +
  geom_sf(data=hwy_nc, col='red')

Counties near the interstate (Buffering)

hwy_nc_buffer = hwy_nc |>
  st_buffer(10000)

ggplot() + 
  geom_sf(data=ncc) +
  geom_sf(data=hwy_nc, color='red') +
  geom_sf(data=hwy_nc_buffer, fill='red', alpha=0.3)

Counties near the interstate (Buffering + Union)

hwy_nc_buffer = hwy_nc |>
  st_buffer(10000) |>
  st_union() |>
  st_sf()

ggplot() + 
  geom_sf(data=ncc) +
  geom_sf(data=hwy_nc, color='red') +
  geom_sf(data=hwy_nc_buffer, fill='red', alpha=0.3)

Example

How many counties in North Carolina are within 5, 10, 20, or 50 km of an interstate highway?

hwy_nc |>
  st_buffer(10000) |>
  st_union() |>
  st_intersects(ncc, y = _) |>
  map_lgl(~ length(.x) >= 1) |>
  sum()

[1] 55

Gerrymandering Example

NC House Districts - 112th Congress

( nc_house = read_sf("data/nc_districts112.gpkg", quiet = TRUE) |>
    select(ID, DISTRICT) |>
    mutate(DISTRICT = as_factor(DISTRICT))
)

Simple feature collection with 13 features and 2 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: -84.32187 ymin: 33.84452 xmax: -75.45998 ymax: 36.58812
Geodetic CRS:  WGS 84
# A tibble: 13 × 3
   ID           DISTRICT                                               geom
 * <chr>        <fct>                                    <MULTIPOLYGON [°]>
 1 037108112001 1        (((-77.32845 35.35031, -77.35398 35.32799, -77.33…
 2 037108112002 2        (((-78.89928 35.12619, -78.89763 35.12859, -78.89…
 3 037108112003 3        (((-75.68266 35.23291, -75.68113 35.23237, -75.68…
 4 037108112004 4        (((-78.77926 35.78568, -78.77947 35.77568, -78.79…
 5 037108112005 5        (((-79.8968 36.38075, -79.89213 36.37108, -79.892…
 6 037108112006 6        (((-80.4201 35.68953, -80.41483 35.68918, -80.411…
 7 037108112007 7        (((-77.59169 34.40907, -77.58699 34.40611, -77.58…
 8 037108112008 8        (((-78.93373 34.95909, -78.94074 34.95789, -78.94…
 9 037108112009 9        (((-80.93058 35.18181, -80.9244 35.16754, -80.921…
10 037108112010 10       (((-81.04032 35.40447, -81.30021 35.4146, -81.287…
11 037108112011 11       (((-84.00768 35.37262, -84.00831 35.37888, -84.01…
12 037108112012 12       (((-80.4996 35.6493, -80.51926 35.63314, -80.5201…
13 037108112013 13       (((-79.90775 36.3818, -79.90694 36.38382, -79.901…

nc_house = st_transform(nc_house, 3631)
plot(nc_house[,"DISTRICT"], axes=TRUE)

Measuring Compactness - Reock Score

The Reock score is a measure of compactness that is calculated as the the ratio of the area of a shape to the area of its minimum bounding circle.

circs = nc_house |> 
  lwgeom::st_minimum_bounding_circle()
plot(circs |> filter(DISTRICT == 1) |> st_geometry(), axes=TRUE)
plot(nc_house |> select(DISTRICT) |> filter(DISTRICT == 1), add=TRUE)

ggplot(mapping = aes(fill=DISTRICT)) +
  geom_sf(data=nc_house) +
  geom_sf(data=circs, alpha=0.15) +
  guides(color="none", fill="none")

Calculating Reock

nc_house |>
  mutate(reock = (st_area(nc_house) / st_area(circs)) |> as.numeric()) |>
  ggplot(aes(fill = reock)) +
    geom_sf() +
    scale_fill_viridis_c()

nc_house |>
  mutate(reock = st_area(nc_house) / st_area(circs)) |>
  arrange(reock) |>
  print(n=13)

Simple feature collection with 13 features and 3 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 123998.5 ymin: 10979.77 xmax: 930346 ymax: 318095.3
Projected CRS: NAD83(NSRS2007) / North Carolina
# A tibble: 13 × 4
   ID           DISTRICT                                         geom reock
   <chr>        <fct>                              <MULTIPOLYGON [m]>   [1]
 1 037108112012 12       (((473814.9 211717.3, 472007.4 209951.4, 47… 0.116
 2 037108112013 13       (((528146.8 292339.5, 528222.3 292562.4, 52… 0.237
 3 037108112003 3        (((911479.9 169543.9, 911621.3 169488.3, 91… 0.266
 4 037108112002 2        (((618780.6 152664.8, 618930.2 152932.2, 61… 0.303
 5 037108112009 9        (((433786.4 160540.2, 434318.7 158946.9, 43… 0.339
 6 037108112008 8        (((615653.2 134126.5, 615013 133993.3, 6147… 0.342
 7 037108112011 11       (((154791.1 191470.8, 154769.4 192168.1, 15… 0.344
 8 037108112006 6        (((481076.7 216074.5, 481553 216028, 481879… 0.378
 9 037108112001 1        (((761514.7 178801.2, 759235.4 176286.8, 76… 0.378
10 037108112005 5        (((529128.7 292213.3, 529538 291136.4, 5294… 0.399
11 037108112010 10       (((424301.6 185435.1, 400728.7 187075, 4018… 0.411
12 037108112004 4        (((629556.3 225844, 629539.1 224734.4, 6281… 0.480
13 037108112007 7        (((739073.9 74030.77, 739510.2 73709.48, 73… 0.624

Raster Data (stars)

Example data - Meuse

( meuse_rast = stars::read_stars(
    system.file("external/test.grd", package="raster")
  ) |>
    st_transform(st_crs(meuse_riv))
 )

stars object with 2 dimensions and 1 attribute
attribute(s):
              Min.  1st Qu.   Median    Mean  3rd Qu.     Max. NA's
test.grd  138.7071 293.9575 371.9001 425.606 501.0102 1736.058 6022
dimension(s):
  from  to              refsys                     values x/y
x    1  80 Amersfoort / RD New [80x115] 178451,...,181611 [x]
y    1 115 Amersfoort / RD New [80x115] 329530,...,334090 [y]
curvilinear grid

stars class

str(meuse_rast)

List of 1
 $ test.grd: num [1:80, 1:115] NA NA NA NA NA NA NA NA NA NA ...
 - attr(*, "dimensions")=List of 2
  ..$ x:List of 7
  .. ..$ from  : num 1
  .. ..$ to    : num 80
  .. ..$ offset: num NA
  .. ..$ delta : num NA
  .. ..$ refsys:List of 2
  .. .. ..$ input: chr "EPSG:28992"
  .. .. ..$ wkt  : chr "PROJCRS[\"Amersfoort / RD New\",\n    BASEGEOGCRS[\"Amersfoort\",\n        DATUM[\"Amersfoort\",\n            E"| __truncated__
  .. .. ..- attr(*, "class")= chr "crs"
  .. ..$ point : logi NA
  .. ..$ values: num [1:80, 1:115] 178451 178491 178531 178571 178611 ...
  .. ..- attr(*, "class")= chr "dimension"
  ..$ y:List of 7
  .. ..$ from  : num 1
  .. ..$ to    : num 115
  .. ..$ offset: num NA
  .. ..$ delta : num NA
  .. ..$ refsys:List of 2
  .. .. ..$ input: chr "EPSG:28992"
  .. .. ..$ wkt  : chr "PROJCRS[\"Amersfoort / RD New\",\n    BASEGEOGCRS[\"Amersfoort\",\n        DATUM[\"Amersfoort\",\n            E"| __truncated__
  .. .. ..- attr(*, "class")= chr "crs"
  .. ..$ point : logi NA
  .. ..$ values: num [1:80, 1:115] 334090 334090 334090 334090 334090 ...
  .. ..- attr(*, "class")= chr "dimension"
  ..- attr(*, "raster")=List of 4
  .. ..$ affine     : num [1:2] 0 0
  .. ..$ dimensions : chr [1:2] "x" "y"
  .. ..$ curvilinear: logi TRUE
  .. ..$ blocksizes : NULL
  .. ..- attr(*, "class")= chr "stars_raster"
  ..- attr(*, "class")= chr "dimensions"
 - attr(*, "class")= chr "stars"

Plotting

plot(meuse_rast)

plot(
  meuse_riv, 
  col=adjustcolor("lightblue",alpha.f = 0.5), border=NA,
  ylim = c(329500, 333611), axes=TRUE
)
plot(meuse_rast, add=TRUE)

ggplot

ggplot() +
  stars::geom_stars(data=meuse_rast) +
  scale_fill_viridis_c()

ggplot() +
  stars::geom_stars(data=meuse_rast) +
  geom_sf(data=meuse_riv, fill="lightblue", color=NA, alpha=0.5) +
  scale_fill_viridis_c() +
  ylim(329500, 333611)

plot(meuse_rast, axes=TRUE)

meuse_rast_ll = st_transform(meuse_rast, "+proj=longlat +datum=NAD83 +no_defs")
plot(meuse_rast_ll, axes=TRUE)

EPSG 3631
Lat / Long

meuse_rast

stars object with 2 dimensions and 1 attribute
attribute(s):
              Min.  1st Qu.   Median    Mean  3rd Qu.     Max. NA's
test.grd  138.7071 293.9575 371.9001 425.606 501.0102 1736.058 6022
dimension(s):
  from  to              refsys                     values x/y
x    1  80 Amersfoort / RD New [80x115] 178451,...,181611 [x]
y    1 115 Amersfoort / RD New [80x115] 329530,...,334090 [y]
curvilinear grid

meuse_rast_ll

stars object with 2 dimensions and 1 attribute
attribute(s):
              Min.  1st Qu.   Median    Mean  3rd Qu.     Max. NA's
test.grd  138.7071 293.9575 371.9001 425.606 501.0102 1736.058 6022
dimension(s):
  from  to                       refsys                   values x/y
x    1  80 +proj=longlat +datum=NAD8... [80x115] 5.721,...,5.767 [x]
y    1 115 +proj=longlat +datum=NAD8...    [80x115] 50.96,...,51 [y]
curvilinear grid

Cropping

meuse_rast_riv = meuse_rast[ meuse_riv ]
plot(meuse_rast_riv, axes=TRUE)

Segmentation

meuse_rast |>
  mutate(bins = cut(test.grd, 3) ) |>
  select(bins) |>
  plot()

Polygonization

meuse_rast_poly = meuse_rast |>
  mutate(bins = cut(test.grd, 3) ) |>
  select(bins) |>
  st_as_sf()
plot(meuse_rast_poly)

meuse_rast_poly |>
  group_by(bins) |>
  summarize() |>
  plot()

meuse_rast_poly |>
  group_by(bins) |>
  summarize() |>
  mutate(area = st_area(geometry))

Simple feature collection with 3 features and 2 fields
Geometry type: GEOMETRY
Dimension:     XY
Bounding box:  xmin: 178431 ymin: 329589.8 xmax: 181590.9 ymax: 333749.8
Projected CRS: Amersfoort / RD New
# A tibble: 3 × 3
  bins                                                      geometry   area
* <fct>                                               <GEOMETRY [m]>  [m^2]
1 (137,671]          POLYGON ((178551 329829.8, 178511 329829.8, 17… 4.56e6
2 (671,1.2e+03]      MULTIPOLYGON (((178711 329829.8, 178751 329829… 4.74e5
3 (1.2e+03,1.74e+03] MULTIPOLYGON (((179790.9 332189.8, 179790.9 33… 5.12e4

Spatial Data andCartography (Part 2)

sf object summary

Plotting

Example Data - NC SIDS

Base Plots

Geometry Plot

Graticules

EPSG 3631

EPSG 3631 w/ Graticules

EPSG 3631 w/ Lat / long Graticules

EPSG 3631 w/ 3631 Graticules

ggplot2

ggplot2 + projections

ggplot2 + viridis

Example Data - Meuse

Meuse

Layering plots

ggplot2

ggplot2 - axis limits

ggplot2 - axis limits

ggplot2 - bounding box

Geometry Predicates

DE-9IM

Spatial predicates

Sparse vs Full Results

Examples

Data

Which counties have an airport?

Which counties have an airport?

Which counties neighbor Durham County?

Which counties have more than 4 neighbors?

Geometry Manipulation

Casting

Casting - POINT

Casting - LINESTRING

Grouping Features

More Grouping

Union via summarize

Affine Transfomations

Scaling Size

Highway Example

Highways

NC Interstate Highways

Counties near the interstate (Buffering)

Counties near the interstate (Buffering + Union)

Example

Gerrymandering Example

NC House Districts - 112th Congress

Measuring Compactness - Reock Score

Calculating Reock

Raster Data (stars)

Example data - Meuse

stars class

Plotting

ggplot

Rasters and Projections

Cropping

Segmentation

Polygonization

Spatial Data and
Cartography (Part 2)

`sf` object summary